r^2=9r-18

Solution for r^2=9r-18 equation:

Simplifying
r2 = 9r + -18

Reorder the terms:
r2 = -18 + 9r

Solving
r2 = -18 + 9r

Solving for variable 'r'.

Reorder the terms:
18 + -9r + r2 = -18 + 9r + 18 + -9r

Reorder the terms:
18 + -9r + r2 = -18 + 18 + 9r + -9r

Combine like terms: -18 + 18 = 0
18 + -9r + r2 = 0 + 9r + -9r
18 + -9r + r2 = 9r + -9r

Combine like terms: 9r + -9r = 0
18 + -9r + r2 = 0

Factor a trinomial.
(3 + -1r)(6 + -1r) = 0

Subproblem 1
Set the factor '(3 + -1r)' equal to zero and attempt to solve:

Simplifying
3 + -1r = 0

Solving
3 + -1r = 0

Move all terms containing r to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -1r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1r = 0 + -3
-1r = 0 + -3

Combine like terms: 0 + -3 = -3
-1r = -3

Divide each side by '-1'.
r = 3

Simplifying
r = 3
Subproblem 2
Set the factor '(6 + -1r)' equal to zero and attempt to solve:

Simplifying
6 + -1r = 0

Solving
6 + -1r = 0

Move all terms containing r to the left, all other terms to the right.

Add '-6' to each side of the equation.
6 + -6 + -1r = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1r = 0 + -6
-1r = 0 + -6

Combine like terms: 0 + -6 = -6
-1r = -6

Divide each side by '-1'.
r = 6

Simplifying
r = 6
Solution
r = {3, 6}